Some necessary context
I think that the two paragraphs preceding the one quoted above provide crucial context for the sentence at issue. Here are the three relevant paragraphs from Justice Blackburn's opinion:
But I have more difficulty about the second point raised in the case. I apprehend that if one of the parties intends to make a contract on one set of terms, and the other intends to make a contract on another set of terms, or, as it is sometimes expressed, if the parties are not ad idem, there is no contract, unless the circumstances are such as to preclude one of the parties from denying that he has agreed to the terms of the other. The rule of law is that stated in Freeman v Cooke. If, whatever a man's real intention may be, he so conducts himself that a reasonable man would believe that he was assenting to the terms proposed by the other party, and that other party upon that belief enters into the contract with him, the man thus conducting himself would be equally bound as if he had intended to agree to the other party's terms.
The jury were directed [by the judge presiding at the trial] that, if they believed the word “old” was used, they should find for the defendant—and this was right; for if that was the case, it is obvious that neither did the defendant intend to enter into a contract on the plaintiff's terms, that is, to buy this parcel of oats without any stipulation as to their quality; nor could the plaintiff have been led to believe he was intending to do so.
But the second direction raises the difficulty. I think that, if from that direction the jury would understand that they were first to consider whether they were satisfied that the defendant intended to buy this parcel of oats on the terms that it was part of his contract with the plaintiff that they were old oats, so as to have the warranty of the plaintiff to that effect, they were properly told that, if that was so, the defendant could not be bound to a contract without any such warranty unless the plaintiff was misled. But I doubt whether the direction would bring to the minds of the jury the distinction between agreeing to take the oats under the belief that they were old, and agreeing to take the oats under the belief that the plaintiff contracted that they were old.
Chief Justice Cockburn had concluded in his opinion that the defendant buyer should be bound to pay for the oats if he knowingly and intentionally agreed to buy that particular item, whether it suited his needs or not, as long as the parties to the contract had not agreed to the condition that the oats be old.
Justice Blackburn's analysis goes somewhat further than the chief justice's. He says that "if one of the parties intends to make a contract on one set of terms, and the other intends to make a contract on another set of terms, or, as it is sometimes expressed, if the parties are not ad idem, there is no contract, unless the circumstances are such as to preclude one of the parties from denying that he has agreed to the terms of the other."
Justice Blackburn then turns his attention to the two "directions" (that is, instructions) that the judge at trial gave to the jury. First, Justice Blackburn notes (and approves of) the trial judge's direction that if the jury found that the defendant buyer had used the word "old" in the contract negotiations with the plaintiff seller, the jury should reach a verdict in favor of the defendant because that expressed (though not written) characterization of the property contracted for clearly indicated the intention of the buyer to buy old oats. Next he considers the trial judge's second direction—which, unfortunately, the Wikipedia article that the OP cites does not reproduce. Here is that part of the record, as reported in Chief Justice Cockburn's opinion:
The learned judge of the county court left two questions to the jury: first, whether the word "old" had been used with reference to the oats in the conversation between the plaintiff and the defendant's manager [who had received and approved the sample oats on the defendant's behalf]; secondly, whether the plaintiff had believed that the defendant believed, or was under the impression, that he was contracting for old oats; in either of which cases he directed the jury to find for the defendant.
This second "direction" is the subject of the sentence that the OP is struggling with.
How should we parse the mysterious sentence?
So now we finally get to the mysterious sentence:
I think that, if from that [second] direction the jury would understand that they were first to consider whether they were satisfied that the defendant intended to buy this parcel of oats on the terms that it was part of his contract with the plaintiff that they were old oats, so as to have the warranty of the plaintiff to that effect, they were properly told that, if that was so, the defendant could not be bound to a contract without any such warranty unless the plaintiff was misled.
The logical block that the OP called out between check marks in the question above is incomplete. The whole idea under consideration is actually this:
whether they were satisfied that the defendant intended to buy this parcel of oats on the terms that it was part of his contract with the plaintiff that they were old oats, so as to have the warranty of the plaintiff to that effect,
This amounts to saying
whether they were satisfied that the defendant intended to buy the specified parcel of oats on the understanding that the contract with the plaintiff stipulated that they were old oats, and thus incorporated the plaintiff's assurance that the oats were old,
The next potentially ambiguous part of the sentence to consider is this:
they were properly told that, if that was so, the defendant could not be bound to a contract without any such warranty unless the plaintiff was misled.
The meaning here appears to be as follows:
the jury were properly told that, if the defendant believed that the age of the oats was specified in the contract, the defendant could not be bound to abide by the actual terms of the contract, which lacked any such specification as to the oats' age, unless the plaintiff was misled as to the defendant's understanding of what was in the contract.
In other words, Justice Blackburn is saying that if the defendant believed at the time that the contract was created that there was agreement as to the oldness of the oats covered by the contract—and not merely that the defendant believed at that time (for whatever uncorroborated reason) that the oats were old—then the instruction to find for the defendant on that basis was valid as a matter of law.
However, he doubts that the distinction between believing that oldness of the oats was a term of the contract and simply believing that the oats were old was adequately expressed to the jury in the wording of the trial judge's second "direction."
As a result—given that the jury's finding in the defendant's favor was not clearly tied to a finding that the seller had promised to supply old oats, and given that a verdict in favor of the defendant on the basis of the trial judge's second instruction might have reflected a misunderstanding of the proper grounds for a valid finding on that point of law—Justice Blackburn joined with Chief Justice Cockburn in remanding the case for a new trial.
Final remarks
The sentence in question is quite long, but what makes it difficult to understand isn't any particularly complex syntax or diction that it contains; rather, the problem is that the sentence alludes to factual details and points of law not contained anywhere in Justice Blackburn's opinion. Once you've identified and sorted out the ideas that are under discussion, interpreting the language itself becomes a fairly straightforward task.
